While I was making my discipline priest, I couldn’t find any source that says one can not wield at the same time (with limitations to each side like how it works in-game) although I was told like you, I will say no one brought an actual source that it’s impossible. On the contrary, although WoW Lore is a mess, there are sources in that mess that Discipline Priests very much exists.
Some priests pride themselves on pragmatism. They understand that light casts a shadow, that darkness is defined by light, and that true discipline stems from one’s ability to balance these opposing powers in services of a greater cause. While these priests possess many holy virtues to aid their allies, they also dabble in the dark arts to debilitate their enemies—always exercising immense discipline to keep themselves away from the brink of insanity. Many would say the ends justify the means; scriptures both virtuous and vile should be studied and understood to protect the congregation.
From Legion, Class Hall stuff
Anduin Wrynn speculated to be a Discipline Priest, as he can wield Light but also uses Mind-Control in a Pandaria quest and uses the Psychic Scream ability currently when Horde invades SW to kill him. Although in-game, both spells are accessible for Holy Priests, most of the time mind-altering spells tend to fall under the school of shadow.
Is there a reason that many priest spells, especially shadow priest spells, have names that refer to psychic phenomena like " [Mind Spike]" or " [Psychic Horror]"? Are priests implicitly telepaths?
The Light is often said to bring about feelings of positive emotion— hope, courage, comfort— and the like. Shadow abilities are just the opposite, able to impart feelings like despair, doubt, and panic. In a poetic sense, it can be said that the emotions which the Light brings about come from the “heart,” whereas the emotions manipulated by shadow are often based on survival logic, and therefore affect the “mind.” That said, priests and their abilities are not necessarily always psychic or telepathic.
(From an interview.)
I hope that was helpful, and I say unless those people bring current sources (and not already retconned stuff) go for it. Although it’s a very small piece, I believe the Legion Artifact Weapon, it’s traits, the whole retconned Light-Shadow/Void stuff at Chronicles proves it’s possible for discipline priests the exist.